Modeling tidal currents beneath Filchner-Ronne Ice Shelf and on the adjacent continental shelf: their effect on mixing and transport

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. C6, PAGES 13,449-13,465, JUNE 15, 1999 Modeling tidal currents beneath Filchner-Ronne Ice Shelf and on the adjacent continental shelf: their effect on mixing and transport Keith Makinson and Keith W. Nicholls British Antarctic Survey, Natural Environment Research Council, Cambridge, England Abstract. A depth-averaged tidal model has been applied to the southern Weddell Sea. The model domain covers the southorn continental shelf, including the ocean cavity beneath Filchner- Ronne Ice Shelf. Reasonable agreement with the available current meter data has been achieved. Our results confirm that in areas with shallow water and large topographic gradients, tidal oscillations with peak velocities up to 1 m s - play a significant role in the vertical mixing and transport of water masses. The estimated energy dissipation beneath Filchner-Ronne Ice Shelf due to surface friction is 25 GW, approximately 1% of the world's total tidal dissipation. Tidally induced Lagrangian residual currents converging at the ice front, an area of strong mixing, draw together water masses from the continental shelf and sub-ice shelf cavity. The model indicates that Lagrangian residual currents have fluxes of up to 250,000 m 3 s 'l, and speeds of over 5 cm s ' along the ice front, with over 350,000 m 3 s ' being exchanged between the sub-ice shelf cavity and adjacent continental shelf. These currents are particularly efficient in ventilating the sub-ice shelf cavity within 150 km of Ronne Ice Front. Such strong tidal mixing will significantly modify the properties of water masses that flow through this region, particularly to the west of Berkner Island. The model predictions indicate that tidal processestrongly influence the oceanographic conditions in the vicinity of Ronne Ice Front. Shipborne observations along the ice front support many of the model predictions concerning the effect of tides on the hydrography. 1. Introduction The continent of Antarctica is fringed by ice shelves, the floating portion of the Antarctic Ice Sheet. Their presence affects both the flow of ice from the continental interior and the hydrography of the adjacent continental shelf. The two largest ice shelves, the Ross and Filchner-Ronne, together form a large part of the West Antarctic Ice Sheet. Located in the southern Weddell Sea, Filchner-Ronne Ice Shelf (FRIS) covers an area of almost 450,000 km 2 [Fox and Cooper, 1994] and is by volume the largest ice shelf, draining 24% of the area of the continent's grounded ice. Ronne Ice Shelf's thickness ranges from around 300 m at the ice front to a maximum of 2000 m at its deep grounding lines. The southern Weddell Sea is of considerable oceanographic interest as Ice Shelf Water (ISW) formed beneath FRIS is ultimately transformed into Antarctic Bottom Water (AABW) in the deep ocean. About 80% of AABW has its origin in this region [Foldvik and Gammelsrod, 1988]. Close to Filchner-Ronne Ice Front the oscillatory action of the tides, the tidal divergence, and the offshore winds act to export sea ice out of the region. Throughout much of the year they maintain a strip of open water, usually called a shorelead, along the ice front [Foldvik et al., 1985; Foldvik and Gammelsrod, 1988]. In this shore lead there is a concentrated production of High Salinity Shelf Water (HSSW) [Gill, 1973], a dense water mass formed by salt rejection during the production of sea ice. In general, the seafloor Copyright 1999 by the American Geophysical Union. Paper number 1999JC /99/1999JC slopes down toward the continental interior, and so the HSSW flows beneath the ice shelf. Once beneath FRIS the HSSW enters an unusual oceanographic environment. Within the sub-ice shelf cavity, water masses are isolated from atmospheric forcing, and tidal and thermohaline processes dominate the circulation. Once the HSSW has descended to the grounding line regions it has an in situ temperature up to 1 øc higher than the pressure freezing point of seawater [Jenkins and Bornbosch, 1995]. Occupying the lower portion of the water column, the HSSW is separated from the ice shelf base by ISW which has a temperature close to the in situ freezing point. MacAyeal [1984a] suggests tidal stirring as a probable mechanism for mixing the HSSW up through the water column into the overlying ISW, thereby sustaining strong melting where the HSSW comes into contact with the base of the ice shelf. Thus tides may play a crucial role in the thermohaline circulation beneath the ice shelf. In addition to their contribution to vertical mixing, tidal oscillations over topographic features drive steady barotropic circulations, or residual currents, that contribute to the large-scale transport of heat, salt, and other tracers. Probably the most significantopographic feature affecting the water column in the southern Weddell Sea is the ice front of FRIS. Across some portions of the ice front, there is a step change of more than 50% in the water column thickness. Strong residual currents are likely to be associated with this step. To determine the contribution of tidal processes to the oceanographic regime in the vicinity of the ice shelf, we apply a high-resolution, depth-averaged tidal model to the southern Weddell Sea. The domain covers the southern continental shelf, including the ice shelf-covered region. The model is driven at its boundary by a larger-scale application of the same code [Smithson 13,449

2 13,450 MAKINSON AND NICHOLLS: MODELING TIDAL CURRENTS 71øS Sea ddell Sea 1 73øS 90 N 75øS Ross Ice Shelf Ronne Depression 77øS Ice Hemmen Ice Rise 79øS Rutford Ice Stream island Filchner Depression 81øS 83os, ice Rise Doake Ice Rumples Henry Ice Rise Filchne r ice Shelf... 1 I! I I I... 90øW 80øW 70øW 60øW 50øW 40øW 30øW 20øW Figure 1. Map showing the model domain. The darkest shading indicates areas of grounded ice, and the lighter shading indicates the floating ice shelf. The contours give the water column thickness in meters. The location and name of current measurement sites used for comparison with the model are marked. The inset indicates the position of Filchner-Ronne Ice Shelf (FRIS) in the southern Weddell Sea, and the box shows the region covered by the model domain. et al., 1996], which in turn is driven at its boundary by the global tidal model of Schwiderski [1980]. In this study we are not concerned with the precise prediction of tides for the region. Rather, we seek to estimate the likely effects of tidal processes on the oceanography of the ice shelf environs. We show that oceanographic observations from along a large section of Ronne Ice Front can be explained by tidal effects and that the oceanographic conditions in some areas of the sub-ice shelf cavity itself are likely to be dominated by tidal, rather than purely thermohaline, processes. First, we presenthe barotropic tidal model used for this study, including a description of the domain. The output from the model includes tidal elevations and currents, of which this paper addresses only the latter. Other authors have already considered tidal elevations in this region [Genco et al., 1994; Robertson et al., 1998; Robinson, 1996; Smithson et al., 1996]. A comparison with the available tidal current measurements is given in section 3. Section 4 presents average tidal currents and mixing energies and discusses how the pattern of basal melting is influenced by tidally induced vertical heat fluxes. The Eulerian and Lagrangian residual currents that result from tidally generated residual vorticity and Stokes drift are presented in section 5. The estimates of tidal mixing and Lagrangian residual currents are used in section 6 to explain some of the features found in hydrographic observations from the shore lead. 2. Numerical Model, Bathymetry, and Results The model used in this study is a finite difference barotropic tidal model in spherical polar coordinates [Smithson et al., 1996] based on depth-averaged equations of continuity and motion discretized onto the model grid. The grid used is the Arakawa "C grid." The domain, shown in Figure 1, lies between latitudes 71 øs and 84øS, and longitudes 15øW and 90øW. This encompasses the entire southern Weddell Sea continental shelf, including the region covered by FRIS. The model grid has a regular spacing of 4' latitude by 15' longitude, corresponding to 7.4 km north-south and ranging from 9 km to 3.4 km east-west. The seabed stress is related to the depth mean current using a quadratic friction law and the coefficient of bottom friction was set to However, beneath

3 MAKINSON AND NICHOLLS' MODELING TIDAL CURRENTS 13,451 the ice shelf area the value was doubled to account for the additional drag at the ice-ocean interface. Apart from providing a second frictional surface and reducing the water column thickness, the ice shelf has no influence on the tides in this model. The horizontal eddy viscosity was taken to be 5.0 m 2 s 4 over the whole domain. The time step At for the integration was set at 15 s to ensure the Courant-Friedrichs-Lewy (CFL) condition, At < As(2gD) 'ø'5, was satisfied throughout the domain. As is the grid spacing, g is the gravitational acceleration, and D is the water column thickness. In this application the model is forced with a time series of sea surface heights along its open boundary. Data for the boundary were obtained by interpolation of results from a regional model [Smithson et al., 1996] that was itself forced by the Schwiderski [1980] model. The time series of sea surface elevation for each node along the boundary were computed using the amplitude and phase of six tidal constituents (Q, O, K, N2, M2, S2). The equations of motion and continuity were solved using an explicit finite difference method. North of 75 o S the bathymetry for the model was taken from the U.S. Naval Oceanographic Office Digital Bathymetric Data Base 5 (DBDB5) data set [Van Wyckhouse, 1973]. In that data set a shallow region known as the Belgrano Bank (73 øs, 50øW), which lies near the continental shelf break, has a minimum water depth of 10 m. The General Bathymetric Chart of the Oceans (GEBCO) data set of Johnson et al. [1983], which includes ship data from Belgrano Bank and recent cruise data from this area (K. W. Nicholls, personal communication, 1998), suggests a minimum of no less than 400 m in this area. In our domain we increased the minimum depth to 400 m, similar to the depth of the surrounding continental shelf. Recent geophysical airborne data from the western Weddell Basin [Labrecque and Ghidella, 1997] suggest that the correct position of the southern section of Larsen continental shelf edge lies as much as 100 km to the east of the DBDB5 position. A correction has not been included in the present model bathymetry. South of 75øS bathymetry and ice shelf thickness data were from the digital data set prepared by Vaughan et al. [1994], updated with more recent seismic data from the areas south of Berkner Island, and Korff and Henry Ice Rises [Johnson and Smith, 1997; Mayer et al., 1995]. In areas not covered by ice shelf, bathymetry and water column thickness are the same. Over these areas the water column thickness ranges from 4000 m in the Weddell Sea basin to less than 250 m on the continental shelf, the shallowest being the Berkner Shelf, north of Berkner Island (Figure 1). Beneath FRIS, however, the model uses the water column thickness, defined as the difference between seabed depth and ice shelf draft [Vaughan et al., 1995]. Here the water column thickness is 100 m or less near Ronne Ice Front, increasing to more than 600 m near some sections of the southern grounding line. Initial model conditions consisted of no currents and an undisturbed sea surface. The model was run for 41.5 days with the elevations and currents being recorded hourly over the final 27.6 days. The recorded time series is long enough for the harmonic analysis method to be used to separate the six constituents that drive the model [Foreman, 1977]. The analysis provided tidal amplitude and phase information for elevations and currents at each grid point in the domain. Tidal elevations obtained using the same model but applied to the entire western Weddell Sea have been discussed by Smithson et al. [1996] and Robinson [1996] and are not discussed further here. Amplitudes and phases of the eastward and northward components of each tidal current constituent predicted by the model were used to construct current ellipses. The current ellipses 71 øs (a) 73øS 75øS 77øS 79øS 81 øs 83øS 71 øs 73øS 75øS 77øS 79øS 81 øs 83øS 90øW 80øW 70øW 60øW 50øW 40øW 30øW 20øW 90øW 80øW 70øW 60øW 50øW 40øW 30øW 20øW Figure 2. Modeled tidal current ellipses plotted at every eighth grid point for the (a) K and (b) M 2 tidal constituents, which are representative of other constituents in the diurnal and semi-diurnal bands, respectively. The lightly shaded regions indicate anticlockwise rotation of the currents. for the main diurnal tide K and the main semidiurnal tide M 2 are representative of other constituents in their band and are plotted every eighth grid point over the model domain in Figures 2a and 2b. Shaded and unshaded areas show anticlockwise and clockwise rotation of current vectors. In the deep Weddell Sea all current constituents are weak, with amplitudes less than 0.02 m s 4. At the continental shelf break, diurnal currents are up to 5 times larger than on the continental shelf. Middleton et al. [1982] observed similar amplification in this region, and attributed it to the presence of diurnal barotropic shelf waves. Over the continental shelf the highest velocities (>0.5 m s 4 for M2) are found in shallow areas, particularly the region south of Ronne Ice Front, close to Berkner Island. There the draft of the ice

4 13,452 MAKINSON AND NICHOLLS: MODELING TIDAL CURRENTS 71øS 3. Available Data and Comparison With Model Results 73øS 75øS 77øS 79øS 81 øs 83øS 90øW 80øW 70øW 60øW 50øW 40øW 30øW 20øW Figure 3. A contour plot of the average RMS water speeds over At the continental shelf break, moorings were deployed and the model domain, with speeds greater than 0.2 m s '] heavily recovered by several different groups over the period 1968 to 1980 shaded. The highest speeds are found in the shallow region south [Elder and Seabrooke, 1970; Foldvik and Kvinge, 1974; Middleton of Ronne Ice Front and Belgrano Bank. et al., 1982; 1987]. Taking site C (Figure 5), which is representative of the six sites in the area, the modeled diurnal currents reproduce the observed amplification seen for K] and Q. Unlike the observedata set, the model shows amplification in O], shelf combines with shallow bathymetry to create a water column most probably the result of incorrect bathymetry along the less than 100 m thick. In shallow areas the ellipses become more continental shelf break and adjacent sea. The absence of O open, indicating a tidal current of nearly constant strength amplification in the observations has been attributed to the throughouthe tidal cycle. Over the continental shelf close to the interaction of diurnal barotropic shelf waves that results from coast the ellipses are greatly flattened, particularly for the semi- variations in the temporal mean velocity field interacting with the diurnal tides, and the major axes are aligned parallel to the nearest irregular shelf topography [Foldvik et al., 1990]. The phase of the coastline. These characteristics are consistent with a Kelvin wave diurnal components are rather poorly reproduced by the model. For propagating around the embayment. MacAyeal [1984b] similarly the semidiurnal currents the model overestimates the amplitudes, interpreted the semidiumal tides in the southern Ross Sea. particularly for M2 and N2, though there is reasonable agreement The modeled tidal constituents were combined and averaged in the phases. over a spring-neap cycle to calculate the average root mean square (RMS) water speed over the domain (Figure 3). Average RMS speeds greater than 0.2 m s ' are highlighted, and average RMS 71 øs spring speeds are typically double the values shown in Figure 3. Of the three regions where the average currents are high, two correspond to areas of relatively shallow water (<200 m): the area 73øS south of Ronne Ice Front and south of Henry Ice Rise. The third region, where the water column is 400 m, is centered on Belgrano Bank. This area is subjecto tidal amplification in the diurnal band 75øS (Figures 2a and 2b) resulting in high RMS speeds. The tidal energy flux vectors were computed over the model 77øS domain using u(gpd r/+pd l u 12), where u is the depth-averaged tidal velocity, D is the water column thickness, r/ is the displacement of the sea surface from the equilibrium level, g is the 79øS gravitational acceleration, and p is the seawater density in this region (1028 kg m'3). The first term representing the work done against gravity during the tidal cycle dominates over the kinematic 81 øs energy term. Figure 4 is a map of the energy flux vectors and shows a proportion of the main energy flux from the Weddell Sea crossing the continental shelf via the Filchner Depression, before 83øS propagating beneath Filchner Ice Shelf. Once beneath the ice shelf most of the flux circulates clockwise south of the ice rises. A small portion branches to the north, between Henry Ice Rise and Berkner Island. Most of the energy beneath the ice shelf is associated with the semidiurnal Kelvin wave that propagates around the embayment. Ice shelves and year-round sea ice cover greatly limit the number of current meter observations from the Weddell Sea. A total of 11 current measurement sites that lie within the model domain are used to validate the model. The current meter sites, shown in Figure 1, fall into three main groups: six continental shelf break sites lying mostly within a concentrated area around 74øS 39øW; three ice front sites positioned close to or up againsthe eastem section of Ronne Ice Front; and two sub-ice shelf sites, of which one is a thermistor cable site. The accuracy of the derived ellipses is chiefly dependent on the lengths of the time series, which are given in Table 1. The table also shows the instrument depth and the tidal species that were extracted. The observed and modeled current ellipses for the constituents extracted from the observed time series are shown in Figure 5. The modeled tidal velocities have been adjusted to account for the difference between the water column thickness measured at the sites and that used in the model domain. 90øW 80øW 70øW 60øW 50øW 40øW 30øW 20øW Figure 4. Average tidal energy flux vectors are plotted for every eighth grid point of the model domain. The majority of the energy flux enters the sub-ice shelf cavity via the Filchner Depression.

5 MAKINSON AND NICHOLLS: MODELING TIDAL CURRENTS 13,453 Table 1. Summary of Current Meter Sites Used for Comparison with the Model Results Site Location Type Instrument Depth, Record Constituents Reference m length, days A Shelfbreak 1815 * 419 Q, On, P, K, N2, M2, S2, K2 Foldviketal. [1990] B Shelf break 620 * 257 Q, O, Pn, Kn, N2, M2, 82, K2 Foldvik et al. [1990] C Shelfbreak 375 * 631 Qn, On, Pn, Kn, N2, M2, S2, K2 Foldviketal. [1990] D Shelf break 400 * 504 Q, On, Pn, Kn, N2, M2, 82, K2 Foldvik et al. [1990] E Shelf break 375 * 257 Q, On, Pn, Kn, N2, M2, 82, K2 Foldvik et al. [1990] F Shelf break 445 * 31 On, K, N2, M2, 82 Foldvik et al. [1990] S 10 Ice front 100 & Kn, M2 Foldvik et al. [1985] Sll Ice front 25 & 75 ' 11 K,M2 Foldviketal. [1985] R2 Ice front 258 & On, Pn, Kn, N2, M2, 82, K2 E. Nygaard (unpublished report, 1995) S2 Sub-ice shelf -$ 660 On, Kn, M2, S2 Makinson and Nicholls [1996] S3 Sub-ice shelf Qn, On, P1, Kn, N2, M2, 82, K2 Makinson and Nicholls [1996] * More than one currentmeter was present at the site; details of the instrument with greatest height above bottom are given, typically 100 m above bottom. The shallowest instrument was believed to be above the draft of the ice shelf. :[: Constituents estimated from thermistor cable data (see Appendix). The three ice front mooring locations used in the model have Indirect observational evidence is available to support the been moved by up to 8 km perpendicular to the ice front to take relative current strengths along Ronne Ice Front. Haase [1986] account of the 1300 m yr 'l advance rate [Vaughan and donas, obtained a transect of surface sediment samples along Ronne Ice 1996]. Using the 1986/1987 ice front position, mooring locations Front within 3.5 km of the barrier that showed a broadiversity of were moved so as to maintain their relative distance from the ice sediments, suggesting a wide range of current environments front. The change in water depth is minimal as the bathymetry is (Figure 3). Over Berkner Shelf the sediments consisted purely of relatively flat at these locations. Two of the three ice front sites, sand. They contained structures typical of a high-energy current S10 and R2, were located a few kilometers offshore of the ice regime, that is, velocities over 20 cm s 'l, 1 rn above the seafloor front. At these sites the modeled constituents are in reasonable over the shallowest areas of Berkner Shelf. Observations by agreement with the observations both in phase and amplitude. Poor Foldvik et al. [1985], like the model results, reveal RMS water agreement between the model and the third ice front site (S 11) is velocities of cm s 'l, with peak spring velocities reaching illustrated in Figure 5, particularly for M2. This probably results 1 rn s 'l. In the area of intermediate water depth ( m) along from either the inability of the model to reproduce the tides the central ice front silt, and clay fractions were found to be high. accurately in close proximity to an abrupt change in the water The high clay content suggests very low velocities of 0-2 cm s 'l. column depth or from the limited length of the record. In addition Over the central ice front section, mean velocities from the model to the ice front moorings, Foldvik et al. [1985] used a Braystoke are 10 cm s 'l, with current measurements within 20 m of the meter close to the ice front to obtain further current data at 20 m seafloor giving essentially the same value (E. Nygaard, Preliminary and 50 m depths. There are differences in the direction of flow results from current measurements in position R2 (76ø29'S, between the model and the data but the ebb and flow of the tide 53 ø00'w) outside the Ronne Ice Shelf in the southem Weddell Sea correspond well both in time and magnitude , unpublished report, Geophysical Institute, BErgen, Beneath the ice shelf, 17 km from the west coast of Korff Ice Norway, 1995) (hereinafter referred to as E. Nygaard (unpublished Rise, Site 3 (S3 in Figure 1) represents the only direct report, 1995))., both higher than suggested by the sediments. On measurement of the sub--ice shelf currents [Nicholls et al., 1997]. the ridge, further to the northwest, the sediments contain mainly The orientations of the modeled ellipses agree with the fine sands, with current ripples indicating water velocities of at observations, and the phases differ by no more than 15 o. However, least several centimeters per second. RMS model velocities were the major axes of the modeled currents are 30% larger than cm s 'l over the ridge. Finally, over Ronne Depression and observed. During conductivity-temperature-depth (CTD) profiling close to the Antarctic Peninsula the gravel and mud content at the site a bottom sensor suggested the presence of small-scale increases. The gravel and drop stones are of glacial origin with the topography that might be responsible for these differences. muds indicating a low current regime. As with the central ice front Currents at Site 2 (S2 in Figure 1) have been estimated from a section, modeled velocities are higher (13 cm s 'l) than suggested thermistor cable suspended beneath the ice shelf. The analysis by the sediments. Two additional sample sites, km from the yielded the lengths of the major axes of the Ol, K M2 and S 2 ice front, exhibit an increase silt and clay, suggesting weaker ellipses and also the phase for each constituent. The method of currents in the deeper waters away from the influence of the ice analysis described in the Appendix. Modeled and inferred major shelf. Modeled RMS velocities offshore from Ronne Ice Front are axes amplitudes and phases generally agree to within 0.2 cm s 'l and generally lower than the ice front currents, and in this way 20 ø, the only exception being the M2 amplitude, which was 25% consistent with the sediment content. (7 cm s 'l) lower than the value derived from the observations. There are several potential sources of error in the model. The

6 13,454 MAKINSON AND NICHOLLS: MODELING TIDAL CURRENTS SITE-C (375 m) S2 (x2) SITE-S10 (100 rn & 224 m) ::" SITE-S11 (25 m & 75 m) ß '"'"..' ::::'; :: cm s - ::: '"...':?./":.'t.>' S2 i;2) i Observed Model deep... - S Observed shallow O1 (x10) K1 (x10) ':"' M2 (x2) SITE-3 (1125 m) Figure 5. Tidal ellipses from the available current meter sites overlain with results from the model. Where the constituent is small a multiplying factor is applied and indicated. The current vector'sense of rotation is indicated by an arrow, and its phase by line from the ellipse center. The orientation of any significant nearby topography and the depth of the instrument are indicated. The ellipses from site C are shown to represent the continental shelf break sites. forcing at the open boundary was provided by a larger area model which used a poorly known bathymetry. In particular, the location of the edge of the Larsen continental shelf was wrong by up to 100 km. The Schwiderski global tidal data set used to force the larger scale model is also likely to be less accurate in this region [Le Provost et al., 1995]. In the present application of the model, the water column thickness over the ice shelf area is subject to errors both in the seabedepth and ice thickness, neither of which are well known at the model resolution. The location of some of the current meter sites is not ideal for testing modeled currents. Examples are sites at the ice front where the water column has a step change in thickness of hundreds of meters leading to significant errors in current phase, amplitude, and rotation. Overall, however, the model has achieved a reasonable fit to the known data, successfully reproducing the general features of the tidal flow. 4. Tidal Energy and Vertical Mixing Beneath the Ice Shelf Tidal currents are likely to be the principal source of energy for mixing in those areas of the southern Weddell Sea isolated from atmospheric forcing by the presence of ice shelves and fast ice. Frictional drag from the seafloor and ice shelf base produces vertical shear, the resultanturbulence causing vertical mixing through the water column. Assuming a quadratic drag law, the rate of dissipation of energy by surface friction E is proportional to the cube of the depth-averaged velocity u and is given by E=Pkl u l u'u. Variables p and k are the density of seawater and the bottom friction coefficient which are assigned the values used in the model run (1028 kg m '3 and ). As in the model run, to account for the presence of the ice shelf base as a second frictional surface, the bottom friction coefficient was doubled for grid points covered by ice shelves. As energy dissipation proportional to the cube of the water speed, areas of high dissipation are spatially similar to those with high currents, that is, areas of shallow water. The potential for ice shelf flexure at the grounding lines to act as a sink for tidal energy was first discussed by Doake [1978]. Such an energy sink is not present in the model used in this study. Although Smithson et al. [1996] found evidence that higher friction coefficients beneath the ice shelf may improve the fit between modeled and observed tidal elevations, predicted tidal elevations and currents modeled by Robertson et al. [1998] and in this study agree reasonably well with observations, suggesting that

7 MAKINSON AND NICHOLLS: MODELING TIDAL CURRENTS 13,455 71øS 73øS 75øS 77øS 79øS 81øS 83øS 90øW 80øW 70øW 60øW 50øW 40øW 30øW 20øW Figure 6. The minimum basal melt rate required to maintain stratification of the water column contoured using a log o scale. Areas where basal melt rate to maintain stratification is above 1 rn yr 4 are highlighted. energy dissipation can be adequately modeled without resorting to additional sinks at grounding lines. These results agree with Vaughan [1995], who also suggests that the tidal flexure of ice shelf margins does not dissipate much energy. From this study the total dissipation over FRIS is 25 GW, nearly an order of magnitude greater than the 3.5 GW dissipated beneath Ross Ice Shelf [MacAyeal, 1984a] and accounting for approximately 1% of the world's total tidal dissipation budget [Tsimplis et al., 1995]. Almost three quarters of the energy is lost in the shallow region south of Ronne Ice Front, with most of the remainder being dissipated south of Henry Ice Rise. The highest dissipations beneath the ice shelf (> 1 W m '2) are near to the eastern end of Ronne Ice Front. Over the adjacent continental shelf, which has a thicker water column and therefore lower water velocities, the dissipation significantly less: a total of 8 GW, half of which is lost in a small area around 73 øs, 50øW. It has been estimated that 1-2% of the tidal energy dissipated at frictional surfaces is available for vertical mixing of the water column [Fearnhead, 1975; Schurnacher et al., 1979]. The power required to mix the water column is the power needed to distribute fresh water melted from the ice shelf base through the water column and is therefore dependent on the melt rate F. The power required is given by 2Fpi3gSD where/3= 1/p (Op/OS) = 0.8 x 10 '3 (%o) '], S is the salinity of HSSW (34.759/oo) in the lower half of the water column, and D is the water column thickness. The power available from tidal dissipation apk I u l u.u, where a (0.015) is the fraction of total energy estimated to be available for vertical mixing. Therefore for a water column to be well mixed, the melt rate F must be less than F m = ap(kl u I u'uy(1/2pflgsd) [MacAyeal, 1984a]. Conversely, in areas where melt rates are greater than Fm, stratification will prevail. Figure 6 shows the pattern of distribution of Fm, rather than deftnative values, based on best estimates of the parameters which can be varied, for example, the fraction and composition of HSSW in the lower portion of the water column [Nicholls and Makinson, 1998]. Direct verification of the extent of a stratified or well-mixed water column is limited by scarcity of observations. Likewise, basal melt rates are poorly known and are normally determined using indirect approaches such as glaciological measurements [Jenkins and Doake, 1991 ], ice shelf temperature profiles [Grosj ld et al., 1992] and oceanographic data [Nicholls and Makinson, 1998]. Near Ronne Ice Front melt rates of rn yr ' have been determined by a number of different methods [Kohnen, 1982; Jenkins and Doake, 1991; GrosJbld et al., 1992]. Here tidal oscillations force warm surface waters beneath the ice shelf, causing rapid melting [Gamrnelsrod and Slotsvik, 1981], particularly during summer months when there is an additional heat input into the offshore ocean water. Despite the high melt rates, the model results predict that the water column will be well mixed, for Fm in these areas is over 10 m yr ' (Figure 6). In areas of the ice shelf cavity where ice crystals form in the water column [Bornbosch and Jenkins, 1995], such as the central Ronne Ice Shelf [Robin et al., 1983; Nicholls et al., 1991], the basal melt rate is negative. The rate of negative melt depends on whether ice crystals are held in suspension, or whether they are deposited on the ice shelf base. Ice crystalsuspended in the water column provide additional buoyancy, and consequently contribute to the stratification [Jenkins and Bornbosch, 1995]. Tidal stirring, when Fm<O, therefore has the effect of enhancing stratification but also of reducing the deposition of ice at the ice shelf base and mixing warmer water up through the water column. Closer to the grounding lines, where the ice shelf is thickest, the pressure freezing point of seawater is depressed by up to 1 øc, and relatively high basal melt rates are possible ifhssw is mixed up through the water column. Indeed, melt rates of between 3.5 and 7 m yr 'l have been calculated within 20 km of the grounding line of Rutford Ice Stream [Jenkins and Doake, 1991; Smith, 1996; Corr et al., 1996]. Here, however, the model predicts thathe water column is stratified, as F>F m (Figure 6). In these areas, the high vertical heat fluxes necessary to maintain such basal melt rates are probably induced by shear between the deeper, warmer water and plumes of ISW rapidly ascending the steep basal slope [MacAyeal, 1984a; lenkins, 1991 ]. Such ISW plumes could be initiated very near the grounding line where the water column finally pinches out, and where tidal mixing is likely to be locally high. The pinching out of the water column is not properly represented at the resolution of this model. An extended region of thin cavity south of Henry Ice Rise leads to Fm exceeding 10 m yr 'l (Figure 6), and a well-mixed water column is therefore likely. In this area the basal melt rate is expected to be high compared with nearby stratified areas. Beneath FRIS, vertical mixing competes with the stratifying influence of basal melting. Tidal fronts separate the abrupt changes in water properties caused by variations in the level of vertical mixing between well-mixed and stratified regions [Simpson, 1981 ]. The balance between tidal mixing and buoyancy input from basal melting therefore determines frontal positions. A tidal front causes an inclination of isopycnals which leads to alongfront geostrophic currents. The model predicts tidal fronts near the ice front where the direction of any induced flow would be along the front towards the southeast (Figure 6). Beneath the ice shelf, however, the small density contrasts that are possible across a mixing front (0.2 kg m '3) are likely to be too weak for the development of frontal flows. 5. Residual Current Generation and Model Results 5.1. Eulerian Residual Currents Unlike the oscillatory component of the tides, tidal rectification causes a net displacement of water parcels over the tidal cycle.

8 . 13,456 MAKINSON AND NICHOLLS: MODELING TIDAL CURRENTS 72øS 74øS 76øS...., :::::::', z,, z, ,,, :[:;::"':::;:;::'.....,...,,......,,,,,...,,,,,...,,,,,,,,,,..,,,.,, _ 78øS 80øS 82øS 75øVV 60øW 45øW 30øW Figure 7. The Lagrangian residual tidal currents obtained by removing the oscillatory components from the time series of water current. These mean currents are strongest over the western continental shelf, along Ronne Ice Front and the western coast of Berkner Island, and south of Henry and Korff Ice Rises. The boxes indicate the regionshown in Figures 10 and 11. Robinson [1981] identified three mechanisms for the generation of tidally rectified flows. He showed that the strength of the flows depends on the horizontal and verticalength scales of topography, and the magnitude of the tidal current constituents. Tidal currents flowing across the step change in water column thickness present at an ice front will generate a residual flow along the barrier with the ice shelf on the left. This current is the Eulerian residual current and can be detected using moored current meters. Robinson [1981] noted that a model will underestimate residual currents if the grid spacing underestimates the topographic gradients. Even if the topographic features are well resolved, the residual currents will be underestimated in areas where the tidal excursion is small compared with the grid size. To improve the estimation of residual currents in the model we increased the node density from 15 to 35 nodes per degree of latitude and from 4 to 8 nodes per degree of longitude. For the area of the ice front this yields a grid spacing of less than 3.5 km. To comply with the CFL condition, the time step was reduced from 15 to 8 s. All other parameters remained the same. As before, harmonic analysis was used to find the phase and amplitude of the principal tidal constituents, giving the same results as the lower resolution model. These oscillatory components were then removed from the modeled currents to reveal the Eulerian residuals. Robinson [1981] found that an adequate approximation for the maximum residual flow at a sharp topographic step such as occurs at the ice front is given by V = 0.15x 10'4(Ah/h)E. l,' is the maximum speed in the flow and is found at the step itself. Ah/h is the depth change ratio of the topographic feature, provided its spatial extent is less than the tidal excursion E, perpendicular to the feature. As an example, water column thickness changes of 300 to 100 m in the ice front region of Berkner Shelf, coupled with 8 km average tidal excursions perpendicular to the ice front, will induce a residual Eulerian velocity of 8 cm s ' parallel to the ice front. The agreement between this value and the model prediction (7-8 cm s ' ) gives confidence that the model resolution in this area is adequate to represent the tidal residuals fully. The only direct determination of the mean Eulerian flow in this region is from current meter deployments close to the ice front on the Berkner Shelf at S 11 and S 10. S 11 was at the ice front itself, and the record showed a mean surface current of 8 cm s ' directed northwest along the ice front. Below the ice shelf draft, however, at a depth of 75 m, the measured mean current was 4 cm s ' to the west. S 10 was located 10 km offshore, close to the center of an offshore gyre in the modeled residuals. The current meter record showed a mean current of approximately 2 cm s ', directed to the northwest at 100 m depth and to the northeast at 224 m depth. For this location

9 MAKINSON AND NICHOLLS: MODELING TIDAL CURRENTS 13,457 the model predicted a residual of 1.5 cm s 4 to the northwest. In both cases the model is in closest agreement with the near surface measurements. In deep water areas with less tidal activity and large topographic gradients, such as Filchner Ice Front, the residuals will be underestimated due to insufficient model resolution. At Filchner Ice Front the average tidal excursion is approximately 1.1 km and the water column thickness changes from 1100 to 600 m. This gives an expected residual current, Va, of 0.75 cm s 'l, compared with the model prediction of 0.25 cm s 4. At the continental shelf break a similar effect is seen where steep gradients and small tidal excursions lead to an underestimation of residual currents by up to 50%. The Filchner Ice Front and the steep continental slope represent an extreme; in most areas the residual currents are adequately resolved. 76.6øS (a) 76.7"S 76.8øS 76.9øS f ' ' I... I... I... I 5.2. Lagrangian Residual Currents In addition.to the Eulerian residual currents a water parcel may 77.0øS experience Stokes Drift resulting from the spatial variations in the characteristics of the oscillatory tidal current. This means that the paths actually followed by a water parcel, which are needed when investigating net fluxes, cannot be determined from Eulerian 51.5"VV 51.0"VV I "VV I O"VV I ' residuals alone. Stokes Drift is typically one third the size and in the opposite direction to the Eulerian residual flow [Loder, 1980]. It is greatest where the rotation of the tidal ellipse reverses across the ice front. The net water parcel motion due to tidal activity is the sum of the Eulerian residual current and Stokes Drift and is the Lagrangian residual current (Figure 7). The Lagrangian motion of water parcels, or tracers, was determined from the hourly Eulerian velocity data from the model by trilinear interpolation onto 2 min intervals. A tricubic spline interpolation gave no significant improvement in the results. Examples of the Lagrangian motion of three tracers over a 35 day period are shown in Figure 8a, illustrating the combination of oscillatory and residual currents. Using a 49 hour low-pass filter,.8os 76'9øS the tracer trajectories were smoothed and are indicated by the 77.0øS ':' heavy lines. In Figure 8b the 44 smoothed tracer trajectorieshow a particular point near the ice front, indicated by a cross, north of which they continue along the ice front, and south of which the 51.5"VV 51.0"VV 50.5"VV 50.O"VV tracers are drawn under the ice shelf. This example illustrates the capacity of the residual tidal currents to transport water into and Figure 8. Examples of Lagrangian tracer trajectories over a 35 day out of the ice shelf cavity. Unlike the purely oscillatory tidal period in the area of the ice front shown by the box in Figure 10. motion, this mechanism is capable of ventilating the cavity well The arrows indicate the direction of flow. (a) Three Lagrangian beyond one tidal excursion. Such exchange across the ice front is tracer trajectories with smoothed trajectories indicated by the not seen by Grosfild et al. [1997] in their thermohaline circulation heavy lines. (b) Smoothed trajectories of 44 tracers with an initial model, in which the ice front acts as a barrier. spacing of approximately 200 m. The plus indicates where tracers In order to determine mean Lagrangian velocities, tracer either remain in open water or enter the sub-ice shelf as the flow bifurcates. trajectories must be averaged over a sufficiently long time period. For each grid node a tracer was introduced every hour for 709 hours, the period of almost exactly two spring neap cycles. The Lagrangian trajectory of each tracer was determined using the depth, water speed, and water flux perpendicular to the western interpolation method described above and recorded over a 100 section of Ronne Ice Front at 55øW. The finite model resolution hour period. Each trajectory was low-pass filtered with a 49 hour makes the step in water column thickness appear as a steep slope, cutoff to remove the oscillatory part of the tide. The displacement with the peak flux centered on the ice front. Over the model of the tracer was calculated over the central 50 hour period. domain strong residual Lagrangian currents are present in three Finally, the mean of all 709 tracer displacements yielded a main areas (Figure 7):, the ice front region of Ronne Ice Shelf, the representation of the mean Lagrangian velocity at the position western continental shelf, and the western coast of Berkner Island. where the tracers were originally introduced. Volume fluxes could then be determined by integrating the product of the mean 5.3. Eastern Lagrangian velocities and water column thickness acros sections. Ronne Ice Front To test the consistancy of the mean Lagrangian circulation, the net volume flux over sections bounded by coastlines were calculated. Several sections, including the front of FRIS, gave net flows close to zero ( < 1000 m 3 s']). Figure 9 shows a cros section of water The greatest depth changes and highest tidal velocities are found along the ice front northwest of Berkner Island (Figure 10) and cause the highest residual velocities of 5.6 cm s ']. This flow (A, in Figure 10) is northwest, parallel to the ice front, with

10 13,458 MAKINSON AND NICHOLLS' MODELING TIDAL CURRENTS 0 E -100.c -200 C3-300 ß E. 0.02, E 10 % 8 x 4 " 2 0 (b) (c) Distance along A - A' (km) Figure 9. A section perpendicular to Ronne Ice Front at 55 øw (A- A' in Figure 11) showing (a) the step change in the water column thickness at the ice front as represented by the model, (b) the mean residual water velocity parallel to the ice front with the peak velocity centered on the ice front, and (c) the mean volume flux across A-A', which totals 250,000 m 3 s 'l. volume transports of up to 135,000 m 3 S '1 at 50øW. North of the ice front there is an elongated clockwise gyre (G 1) parallel to and centered km from the ice front. The gyre extends up to 50 km northeast from its center and has a circulation time of about 50 km in diameter, merge to form a larger anticlockwise circulation. To their west residual currents are associated with the submarine ridge. Two inflows (K and M) are located at 55.4øW (50,000 m 3 s 'l) and at 57.3 øw (70,000 m 3 s'l), with two outflows (J and L) located at 54.3øW (175,000 m 3 s 'l) and at 56.8øW (20,000 m 3 s'l). There is a point of convergence of residuals at the ice front, centered on 53.5øW. West of this point, water masses flow parallel to the ice front toward Ronne Depression. To the east, between 52øW and 53øW, there is a broad outflow (N, 20,000 m 3 s 'l) which becomes incorporated into the Berkner Shelf offshore gyre (G 1, Figure 10) Continental Shelf Over the continental shelf, close to the peninsula, a substantial southerly flow (1.4 cm s 'l and 500,000 m 3 s 'l) extends from 71 øs (the model boundary) to 74øS (Figure 7) where the majority tums to the east and joins the northern tip of the gyre from the western Ronne (G2, Figure 11). In a similar model that extends to the northern tip of the Antarctic Peninsula, the flow appears to originate as far north as 69øS [Robinson, 1996]. The region around Belgrano Bank is part of the continental slope where there is significant diurnal amplification, and steep topographic gradients, resulting in strong residual currents. A large anticlockwise circulation dominates the residual current pattern over the western continental shelf north of FRIS (Figure 7). Reducing the gradient of the continental slope in this region by 50% has the effect of reducing both the diurnal amplification and residual currents by a similar proportion, though the overall flow regime remain similar. The only other location where residual currents flow south on to the continental shelf is at 74øS 43øW. There the velocities are lower, cm s -]. Over the open ocea no account is taken of any thermohaline or wind-driven circulation which are poorly known. Estimates by Gill [1973] suggest velocities of the order of centimeters per second; consequently, residual currents will be modulated with currents driven by other processes. During 1986 three huge icebergs broke away from Filchner Ice Shelf [Ferrigno and Gould, 1987], two of which became grounded on Berkner Shelf between 40-45øW and 76-77øS. The model was used to determine their effect on the residual currents, assuming that the icebergs were grounded over their entire area. Without the grounded icebergs, the residual currents in this area are not significant. With them, weak residual currents form an anticlockwise flow around the bergs. Ungrounded parts of the bergs would effectively form ice front type features and have strong associated residual flows. 1 year. The return Lagrangian volume flux (B) associated with this Berkner Shelf gyre is 175,000 m 3 s 'l at up to 2 cm s 'l. Beneath the ice shelf, complicated topography results in several eddies that transport water into and out of the sub-ice shelf cavity. The only outflow (C) in this region lies between 49 ø and 49.5øW (20,000 m 3 s'l). At two locations, water flows from the shore lead into the cavity. Between 50.8øW and 51.8øW the flow along ice front diverges, with one branch forming a diffuse inflow (D) of 80,000 m 3 s 'l. Further to the easthe second inflow (E) of 55,000 m 3 s -I is concentrated along the western coast of Hemmen Ice Rise before it is joined from the west by a 35,000 m 3 s 'l flow. This combined 5.6. Ice Shelf Cavity flow then continues southwards along the Berkner Island coast. The flow around Berkner Island (Figure 7), is the largest 5.4. Western Ronne Ice Front residual flow entirely beneath the ice shelf. At 78øS the peak velocity is 3 cm s 'l with a flux of 90,000 m 3 s 'l. As the water The largest along-ice front flux (F in Figure 11) is situated between the center of Ronne Ice Front and the submarine ridge to the east of Ronne Depression. There between 150,000 and 300,000 column thickness increases, velocities decrease but the volume flux increases to over 100,000 m 3 s 'l. The increased flux results from the addition of weak easterly residual flows set up along the water m 3 s 'l flows parallel to a 100 km length of the ice front. The overall column contours in the central Ronne Ice Shelf. At the southern tip structure consists of anticlockwise and clockwise gyres either side of the barrier. Centered km from the ice front, the offshore gyre (G2 in Figure 11) is relatively diffuse, extending more than 100 km to the northeast from its center. Typically, velocities of 0.5 to 1 cm s '1 give a circulation time of 2.5 years. The total flow northeastowards the continental slope from the ice front (G) is 330,000 m 3 s 'l. The corresponding inflow (H) is 280,000 m 3 s 'l at 0.6 cm s 'I. Beneath the ice shelf two large circulations, each 40- of Berkner Island peak velocities are only 0.5 cm s 'l in the 500 m water column. Beyond this point the flow tums to the east and north following the coast at velocities of between cm s 'l, until eventually crossing the Filchner Ice Front with a flux of 125,000 m 3 s 'l and continuing northward. The time taken for a water parcel to travel to the southern tip of Berkner Island is approximately 2 years, with another 8 years needed for it to arrive at the Filchner Ice Front.

11 MAKINSON AND NICHOLLS' MODELING TIDAL CURRENTS 13,459 Weddell Sea 76.5øS 77.0øS 77.5øS 78.0øS 54øVV 52øVV 50øVV 48øVV 46øVV Figure 10. Smoothed Lagrangian residual trajectories over a 7 day period in the region of Berkner Shelf. Grounded ice is represented by the darkest shading, and floating ice shelf is represented by the lighter shading. The contours are of ice shelf draft at intervals of 50 m. The box marks the region shown in Figure 8. Korff Ice Rise, Doake Ice Rumples, and Henry Ice Rise make most dense over this area [Vaughan et al., 1995], typically every up the areas of grounded ice that occupy the southern central 5-10 km providing increased confidence in the model results. region of Ronne Ice Shelf (Figure 1). Between these areas of Elsewhere, uncertainties in the water column thickness greatly grounded ice there are three channels, 5-20 km wide with a water reduce confidence in the detailed model predictions. Nevertheless, column of approximately 50 m, connecting the central and the types of structure in the modeled residual current field, and southern Ronne Ice Shelf cavity. These channels have high strength of the flows, are expected to be representative of the actual residual currents of up to 6 cm s '1 with associated flows of between residual currents. 3 and 6000 m 3 s '1 yielding a total flux of 10-15,000 m 3 s '1 from the southern trough to the central Ronne Ice Shelf. Either side of the channels and around the ice rises the residual currents mainly 6. Impact of Tidal Processes on Hydrography constitute a series of headland eddies. To the south of the ice rises and Ice Shelf Morphology there is a weak westerly flow (0.5-3 cm s '1 and 30-60,000 m 3 s ' ) found principally along the southern coast of the trough and Filchner-Ronne Ice Front encompasses a wide range of current comprising several eddies. There are also many vigorous gyres that environments with different oceanographic processes, such as are restricted to small coastal features and which do not contribute thermohaline circulation, residual currents and mixing, dominating to the larger scale transport. certain sections of the ice front hydrography. We now consider Over the southern Weddell Sea continental shelf and FRIS, only how mixing and the residual currents predicted by the barotropic sparse bathymetric data are available because of the inaccessibility model would be expected to affect the distribution of tracers of the region. In the western Weddell Sea, heavy sea ice conditions (temperature and salinity) observed at Filchner-Ronne Ice Front, persist throughout the year, greatly limiting shipborne and the topography of the ice shelf itself in the vicinity of the ice observations. Beneath FRIS itself the geometry of the sub-ice shelf front. CTD data have been collect6d along the ice front during cavity can be determined only by a combination of seismic surveys several cruises over the last 30 years: USCGC Glacier in 1968 and ice thickness data. The most tidally active regions beneath the [Elder and Seabrooke, 1970] and in 1973 [Carmack and Foster, ice shelf also have the shallowest water column, particularly in the 1975]; R/V Polarsirkel in 1980 [Foldvik et al., 1985]; Polarstern region of the eastern Ronne Ice Front. Seismic data coverage is in 1984 [Rohardt, 1984]; and R/V Lance in 1993 [Gammelsrod et

12 13,460 MAKINSON AND NICHOLLS' MODELING TIDAL CURRENTS 75.0øS i 75.5øS 76.0øS 76.5øS 60ow 58øW 56øW 54øW 52øW Figure 11. Smoothed Lagrangian residual trajectories over a 7 day period in the region of the western Ronne Ice Front. The ice shelf is represented by the shaded region and the contours give the ice shelf draft. al., 1994]. All the hydrographic surveys were conducteduring the austral summer months with the last three spanning the majority of the Filchner-Ronne Ice Front Tidal Oscillations and Mixing CTD measurements in tidally active regions are often affected by the tidal state during the measurement. One cause of this is the presence of horizontal gradients in the measured properties over the extent of the tidal excursion. Such gradients are likely near the ice front: the sudden change in water column thickness gives strong gradients in tidal energy available for vertical mixing, introducing the possibility of tidal fronts. The difference in the temperature of the water being mixed down from the upper boundary on either side of the ice front, especially during the austral summer, will also compound the effect. The motion of mixing fronts back and forth across the ice front means that the results of CTD measurements made in the shore lead will be strongly influenced by the state of the tide. As an example, during spring tides on Berkner Shelf, measurements made at the ice front toward the end of a period of inflow would be sampling water that was previously 5 km offshore. Conversely, at the end of an outflow, the water being sampled will have originated up to 15 km beneath the ice shelf. Yo-yo CTD stations close to the ice front occupied on Berkner Shelf at 50 ø 07'W [Foldvik et al., 1985] and 50 ø 40'W [Rohardt, 1984] show that during periods of outflow there is a cooling throughout the water column, typically by a few tenths of a degree, but in extreme cases by up to 1 øc in near surface waters. An additional effect influencing ice front CTD measurements results from the combination of strong mixing beneath the ice shelf and the purely periodic advection of water back and forth across the ice front. As the flow field is not completely reversible due to mixing, this is likely to result in an efficient horizontal transfer of tracers into and out of the cavity, but with no net water flow [Wunsch, 1996] Residual Currents In the remainder of this section we consider the effects of the transfer of water itself by the residual tidal currents described in the last section. Away from the ice front the tidal residuals are much weaker, and in the absence of knowledge of the wind or buoyancy-forced flow over the continental shelf it is not clear whether they are significant. We therefore concentrate on the ice front region, where most of the CTD stations have been located. The salinity and potential temperature sections compiled by Foldvik et al. [1985] are shown in Figures 12a and 12b and will be used for reference, together with smoothed Lagrangian trajectories over a 6 week period along the whole Filchner-Ronne Ice Front region (Figure 12c) Ice Shelf Cavity Outflows Between 48øW and 51 øw, the modeled residual flow at the ice front is almost parallel to the barrier (Figure 10), though there is a net outflow from beneath the ice shelf. Outflowing water would

13 MAK1NSON AND NICHOLLS: MODELING TIDAL CURRENTS 13,461 Ronne Submarine Berkner Berkner Filchner Depression Ridge Shelf Island Depression OO øW 55øW 50øW 45øW 40øW 35øVV (c) 65øW 60øW 55øW 50øVV 45øW Figure 12. Sections of (a) salinity and (b) potential temperature along the ice front from Ronne Depression to the Filchner Depression [after Foldvik et al., 1985]. The bathymetry is represented by the darkest shading, and the ice shelf draft is indicated by the lighter shading. (c) Lagrangian trajectories over a 6 week period in the region of Filchner-Ronne Ice Front. The contours are of water column thickness at intervals of 100 m. normally be expected to show signs of glacial melt in the potential temperature-salinity (0-S) signature, and it is surprising that only one of the yo-yo sites located at the ice front revealed ISW in the water column during the outflow part of the tidal cycle [Foldvik et al., 1985]. The S and 0 sections presented in Figure 12 show no evidence of a steady ISW presence in this region, and it is unclear whether there are indeed no tidally driven outflows, or whether they simply do not contain ISW. The offshore gyre (G1) in this region would be expected to increase the residence time of water on the Berkner Shelf, thereby increasing the water's salinity through sea ice formation. West of 54øW, Foldvik et al. [1985] and Rohardt [1984] observed three ISW plumes emerging from beneath the ice shelf at 54.2øW and 56.8øW on the submarine ridge and at øW in Ronne Depression. Garnrnelsrod et al. [1994] observed ISW in the same locations but did not differentiate between the two western plumes, possibly because of the lower density of CTD stations in that area. At 53.25øW, modeled residual currents converge on the ice front, before diverging along the ice front to the east and west (Figure 11). West of this point any ISW emerging from beneath the ice shelf will remain close to the ice front, trapped by the flow parallel to the barrier. The modeled Lagrangian residuals predict a strong outflow between 53.9øW and 54.5øW (J) and weaker outflow associated with the submarine ridge between 56.7øW and 57øW (L). These predicted outflow locations agree with the positions of the ISW plumes observed by Foldvik et al. [ 1985], Rohardt [ 1984], and Gamrnelsrod et al. [ 1994]. Using the model to predict the tidal state when CTD measurements were made along the western Ronne Ice Front, the observed hydrographic features do not appear to be the result of periodic

14 13,462 MAKINSON AND NICHOLLS: MODELING TIDAL CURRENTS tidal excursions. Residual current outflows might therefor explain the two eastern ISW plumes observed by Foldvik et al. [1985] (Figure 12). The westernmost ISW plume (58øW) appears unlikely to be primarily the result of residual tidal currents: the residual outflow at this location is weak, at about 0.3 cm s 4. The section in Figure 12b shows that unlike the two eastern plumes which have their temperature minima at, or close to, the seafloor, the western outflow is centered around 250 m with Western Shelf Water (WSW) below it. This structure suggests an outflow underlain by an inflow, which is not consistent with a tidally forced barotropic current. We therefore suggesthat the western plume is driven primarily by thermohaline processes Ice Shelf Cavity Inflows In areas where inflows are anticipated, CTD sections at the ice front will give few indications. The maximum in the water temperature between the two eastern ISW plumes around 55.2øW (Figure 12b) [Foldvik et al., 1985; Rohardt, 1984] is consistent with warmer offshore waters being drawn beneath the ice shelf. Figure 11 shows the residual currents in the ice front region overlaid with contours of ice shelf draft, indicating a good correlation between thinner ice shelf and the route of the inflows K and M. Further to the east on Berkner Shelf, the model predicts inflows between 50.8øW and 51.8øW (D in Figure 10) and along the westem side of Hemmen Ice Rise (E in Figure 10). The westem inflow (D) appears to be associated with a thinning of the ice shelf. We believe that the thinning in the ice shelf is a result of preferential melting associated with relatively warm, tidally driven inflows. As residual currents are topographically steered, ice shelf thinning will, to some extent, influence the route of the residual flows, but the primary control on the water column thickness in these areas is the bathymetry Modified Weddell Deep Water Intrusion Foldviket al. [1985] and Gammelsrod et al. [1994] interpreted the temperature maximum on the western slope of Berkner Shelf as an intrusion of Modified Weddell Deep Water (MWDW) formed by mixing Winter Water (WW) and Weddell Deep Water (WDW). Foster and Carmack [1976] observed the intrusion of MWDW on the continental shelf at 40øW, up to 100 km from the shelf break. Gamrnelsrod et al. [1994] suggested that from the continental shelf break, a distance of about 450 km from the ice front, a geostrophically balanced flow of MWDW followed the 400 m isobath to the ice front, before appearing to flow beneath the ice shelf. Associated with the 400 m isobath the model gives a very weak southwesterly residual current ( cm s -l)(figure 12c) that might contribute to the transport of MWDW across the continental shelf. The sloping isopycnals associated with the MWDW between 52øW and 53.7øW, which can be seen as sloping isohalines in Figure 12a, suggest a southward flow beneath the ice shelf. Predicted residual currents in the area, however, range from zero up to 0.8 cm s 4 parallel to and slightly away from the ice front. In the vicinity of the intrusion, the ice shelf thins significantly, probably as the result of melting by the MWDW combined with the effects of the western inflow (D) on Berkner Shelf. Offshore from the ice front region, the width of the MWDW intrusion has not been measured. The residual currents at the ice front on Berkner Shelf will force water northwest along the barrier, restricting the easterly extent of the MWDW intrusion at the ice front to approximately 51.5øW. From the model results (Figure 12c) MWDW joins the two dominant offshore gyres (G1 and G2). In CTD sections perpendicular to the ice front at 49øW and 51 øw, Foldvik et al. [1985] observed MWDW warmer than -1.4øC at km from the ice front, suggesting that the MWDW is directed away from the ice front, consistent with the modeled residual gyre G1. Evidence for MWDW entrainment into the westem gyre (G2) can be found in data from a station at 54 øw as a small warm core ( øc) 10 km from the ice from [Foldvik et al., 1985] Contribution of Residual Currents to Mass Transport Along the entire Ronne Ice Front, the contribution of residual currents to water mass transport appears to be comparable to thermohaline driven flows. Observations by Nicholls et al. [ 1997] indicate a 200,000 m 3 s ' thermohaline inflow of WSW that enters the deep sub-ice shelf cavity via the Ronne Depression. After transformation to ISW, this water mass is presumed to emerge from beneath the ice shelf as the plume in the Ronne Depression. Away from the Ronne Depression, in the tidally active regions of Ronne Ice Front, modeled residual currents exchange approximately 250,000 m 3 s - across the ice front, between the sub-ice shelf cavity and open sea. Along Filchner Ice Front the model predicts a weak northward current ( cm s 'l, 125,000 m 3 s 'l) at the westem side of the depression. Observations by Foldvik et al. [1985] show corresponding ISW cores emerging at a similar locations. However, modelling of thermohaline circulations in this region by Grosfeld et al. [1996] and geostrophicalculations by Carmack and Foster [1975] gave fluxes of approximatly 400,000 m 3 s - entering and leaving the ice shelf cavity. Also, Foldvik et al. [ 1985] derived an ISW flow of about 106 m 3 s ' at the shelf break associated with Filchner. Depression. As in the case of the Ronne Depression, we suggest that the hydrography along Filchner Depression is dominated by thermohaline processes, tidal residuals playing a minor or insignificant role. 7. Summary and Conclusions A depth-averaged barotropic tidal model has been used to simulate the tidal currents of the southern Weddell Sea with no accountaken of thermohaline or wind-driven processes. In total, six tidal constituents (Q, O, K, N2, M2, S2) were modeled. There is reasonable agreement between the results from the model and the limited number of available current meter records, given the potentially large errors in bathymetric and ice shelf thickness data used to determine the water column thickness, particularly away from the Filchner-Ronne Ice Front region where only sparse data coverage is available. The largest deviations between measurements and model are found in the diurnal band. However, the model results demonstrate that both oscillatory and residual tidal currents play an important role in the oceanic processes beneath and in the vicinity of Filchner-Ronne Ice Shelf. The strongest tidal currents are found on Berkner Shelf along Ronne Ice Front. Where the ice shelf significantly reduces the water column thickness, tidal currents peak at over 1 m s ' during spring tides. In this area, tidal excursions of up to 15 km beneath the ice shelf, and up to 5 km in the open sea, help maintain a shore lead and therefore the production of HSSW. Energy dissipation by bottom friction is highest in shallow water regions, particularly beneath the ice shelf where the total energy dissipation, approximately 25 GW, accounts for almost 1% of the global energy budget [Tsirnplis et al., 1995]. A consequence of the energy dissipation vertical mixing through the water column, close to the ice fronthis sustains observed melt rates of up to 6 m yr 4. In the deeper regions of the ice shelf cavity where energy dissipation

15 MAKINSON AND NICHOLLS: MODELING TIDAL CURRENTS 13,463 is low, vertical mixing is likely to play only a small role in modifying the water column structure. The application of this depth-averaged model has also yielded a description of the tidally generated residual currents which have been supported by the available ice front observations. These appear to play an important role in the transfer of water between the sub-ice shelf cavity and the adjacent continental shelf. Along the eastern section of Ronne Ice Front the water column thickness reduces from 250 m to less than 100 m. Modeled Lagrangian residual currents reach mean velocities of 5 cm s 4 in this area. Further to the west these currents transport up to 250,000 m 3 s 'l along the ice front. In addition to the along ice front flows there are a number of specific locations where Lagrangian residual currents transport water masses into and out of the sub-ice cavity of FRIS. The rate of exchange totalling approximately 350,000 m 3 s 'l is less than estimates attributed to thermohaline circulation but are of the same order. Shipborne hydrographic observations along the ice front support many of the model predictions. Lagrangian residual flows from the cavity coincide with observations of ISW plumes, and ice shelf thinning coincides with flows entering the cavity, consistent with warmer offshore water being imported and causing preferential melting. Along 350 km of Ronne Ice Front the combination of strong residual currents, large tidal excursions and vigorous mixing give rise to a region where strong melting is both predicted by the model and seen in observations. Along this section of ice front and up to 70 km inshore, melting averages 2-3 m yr 4 [Kohnen, 1982; Jenkins and Doake, 1991; Grosfeld et al., 1992], giving a net loss of km 3 yr 4, equivalent to cm yr 4 over the whole FRIS. Away from the ice front, where residual currents are weaker, it is unclear to what extenthey influence the hydrography. Over the open ocean the effect of tidal residuals will combine with the wind and thermohaline forcing; it is not clear which affect will dominate. In the deep water areas beneath FRIS, particularly the Filchner and Ronne Depressions, residual currents are weak, and we assume thermohaline flows dominate. The largest residual flow that penetrates deep beneath the ice shelf transports approximately 100,000 m 3 s 'l of water anticlockwise around Berkner Island. The flow originates on the Berkner Shelf, west of Berkner Island, and finally emerges from beneath the western end of Filchner Ice Front. Direct confirmation of this current is not yet available. Probably the most important result from this study has been to show that tidal processestrongly influence the oceanographic conditions in the vicinity of Ronne Ice Front and can explain many of the observations made in the shorelead. The combination of vigorous mixing, large tidal excursions, and strong Lagrangian residual currents has a dominant effect on the hydrography beneath about 60% of Ronne Ice Front. Appendix: Extraction of Tidal Constituents From Site 2 Thermistor Cable Data An example portion of the 22-month thermistor cable record is shown in Figure A1. The amplitude of the signal at twice tidal frequency increases down the water column. Assuming the signal is due to the cable swinging in the tidal flow, the most accurate temperature profile through the water column will be given when the temperatures reach a local maximum, that is, when the cable is hanging vertically (we expect the temperature to increase monotonically with increasing depth [Nicholls, 1996]). A "demodulated" record of temperature profiles was therefore obtained by selecting those profiles for which the deepest thermistor showed a local maximum value. After appropriate filtering, a 22-month record of water column temperatures was obtained [Nicholls, 1996]. It was then possible to determine the depth of each thermistor at each of the samples between those times the cable was assumed to be vertical. The way a cable hangs in a vertically uniform current can be described by dt* dl* - (c* + sin (0)) cos (0) d(0) _ cos2(0)-c *sin(0) dl* T* where T*(/), c*, and l* are the nondimensional tension in the cable, the cable's weight per unit length, and the distance along the cable from the bottom end, respectively. They are nondimensionalized by using the length of the cable L and the force per unit length F exerted on the vertically hanging cable by the water flowing at a speed U. Here 0(l) is the angle between the cable and the downward vertical. F is given by F = Cap U2a. Here Ca is the drag coefficient for a cylinder, taken to be 1.0 [see, e.g., Batchelor, 1967], p is the density of seawater, and a is the radius of the cable. By using the value of the weight suspended at the bottom of the cable as an initial value for the tension, and zero as the initial value for 0, the equations were integrated from the bottom up to the ice E Days into 1992 Figure A1. Excerpt from the 22-month time series from the shallowest thermistor (bottom trace) and the deepest thermistor (top trace) from the thermistor cable at Site 2 (S2 in Figure 1). Four-times-daily oscillations in the upper trace indicate that the cable is swinging in a primarily semi-diurnal tidal current. Spring-neap variability is visible in the record.

16 13,464 MAKINSON AND NICHOLLS: MODELING TIDAL CURRENTS shelf base using a Runge-Kutta algorithm. For a given water speed U the vertical position of each thermistor could then be predicted. Using the record of thermistor depths, the results of the simple model of the way the cable hangs yields 10 records of water speed. As the vertical motion was the greatest for the deepesthermistor, this speed record was used for the extraction of tidal constituents. A synthetic speed record was created by making initial guesses for the phase and magnitude of the four tidal constituents that are largest in the Weddell Sea region: O, K, M2, and S2. The mean square deviation between the synthetic speed record and the record Foster, T.D., and E.C. Carmack, Frontal zone mixing and Antarctic Bottom Water formation in the southern Weddell Sea, Deep Sea Res., 23, , Fox, A.J., and A.P.R. Cooper, Measured properties of the Antarctic ice sheet derived from the SCAR Antarctic digital database, Polar Rec., 30, , Gammelsrod, T., A. Foldvik, O.A. Nost, O. Skagseth, L.G. Anderson, E. Fogelqvist, K. Olsson, T. Tanhua, E.P. Jones, and S. Osterhus, Distribution of water masses on the continental shelf in the southem Weddell Sea, In: the Polar Oceans and obtained from the cable was then calculated. This error was Their Role in Shaping the Global Environment, The Nansen minimized using a minimization routine to explore the eightdimensional space formed by the phase and amplitude of the four constituents. Several different initial guesses were made to locate all the likely minima in the error field, and the solution with the smallest minimum error was finally selected. As the cable is able only to give speed information, the phase of the entire set of Centennial Volume, Geophys. Monogr. Set., vol. 85, edited by O.M. Johannessen et al. pp , AGU, Washington, D.C., Gammelsrod, T., and N. Slotsvik, Hydrographic and current measurements in the southern Weddell Sea 1979/80, Polarforschung, 51(1), , constituents contains a 180 ø ambiguity. The principal assumptions Genco, M.L., F. Lyard, and C. Le Provost, The oceanic tides in the inherent in this method are that the tidal velocity is constant throughout the water column, the size of the minor axes of the tidal ellipses for each constituent is small compared with the major axes, and that the tidal ellipses are all oriented in the same direction. South Atlantic Ocean, Ann. Geophys., 12, , Gill, A.E., Circulation and bottom water production in the Weddell Sea, Deep Sea Res., 20, , Grosfeld, K., N. Blindow, and F. Thyssen, Bottom melting on Filchner-Ronne Ice Shelf, Antarctica, using different measuring Acknowledgments. 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